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need different types of voting.
PoliticalSim software

Future Rules

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Single-Winner Elections
STV3Con: STV then Condorcet
Candidate Withdrawal Option
Multi-Winner Elections
STV-C: STV then Condorcet
CPO-STV: Comparison of Pairs of Outcomes by STV
Minimum Rank Group
Unequal reps
Enacting Policies
Voters weight their priority issues
LORr or LORo may reduce effects of elimination order
Funding Projects
Minority Funding Process
How to conduct an MFP vote
Joint Allocation Rule
Maximum Utility Rules
Standardized Scores
Agent Allocation Rules
Comparing funding systems
Setting Budgets
Minority power in setting departmental budgets

Single-Winner Elections

STV3Con, STV then Condorcet

STV3Con, STV Then Condorcet: Condorcet's rule risks electing an unknown.  If the voters are polarized, they may give first choice to a favorite, last to her main rival, and rank many candidates in between -- not thinking how bad or bizarre an unknown might be in office.  This risk could be reduced by using STV to select the [3] candidates with most first- and second-place votes, then testing them 1 against 1 to elect a winner.

Unfortunately STV3 usually picks a triangle of reps, none of whom is near the center.  So a central candidate would be squeezed out by STV3 even if she is broadly (not intensely) popular.

STV5 is more likely to pick 1 candidate near the center -- who is then sure to win the Condorcet runoff.  The winning strategy is to be the 1 most popular with the central voters.  Breadth of support is not important; so in political incentive and effects, this rule more like IRV than Condorcet.

STV7 might select 2 central candidates, and the broader 1 will win the Condorcet comparisons.  But if the top 2 candidates gather 80% of the first-place votes, the other 5 selected might be political weaklings and if 1 of them wins, would she have a mandate to govern, a solid base of support, or the respect of the legislature?

Perhaps a threshold rule could simply require each candidate to win 10 to 20 percent of the first-place votes in order to enter the Condorcet pairwise comparisons.  (The chapter on Candidate Withdrawal Option (CWO)

A standard IRV tally produces an initial winner. Losing candidates may then withdraw and the ballots are re-tallied without them.  The most obvious one to withdraw is the runner-up who lost the final 1 against 1 contest.  She may hope that a candidate closer to her side of the center can beat the initial winner.  Thus CWO may elect a candidate more central than the IRV winner.

If her withdrawal could change the result, a losing candidate might bargain on key political policies with those who stand to win the election and with those who could lose.  Some people want to avoid giving politicians more backroom power to choose the winners of elections.

Also known as a Standing-Down Option or Just-In-Time Withdrawal, this was developed by several people to modify several voting systems.

Multi-Winner Elections

STV-C, STV Interest Groups, then Condorcet

To blend Condorcet's rule more completely within STV: After the STV tally, divide ballots into [seats] electorates. Each electorate has the voters who gave weight to 1 of the STV winners. (A ballot whose weight helped 2 winners has a fraction of a vote in each of those electorates.)

Conduct a Condorcet tally for each little electorate. Using Condorcet's rule for these mini elections may reduce negative campaigns among rivals with similar positions.

Still, chances are the same candidates will win again because each mini electorate is centered around one of the STV winners. STV-C does not ensure electing the overall Condorcet winner -- unless she is exempt from elimination.

The rule's complexity might give its winners dubious mandates. Eventually it may be added to PoliticalSim for testing. For now, the “Release” option probably gives the same result.

CPO-STV: Comparison of Pairs of Outcomes by STV

T. Nicolaus Tideman has created a rule that surpasses STV-C at blending the qualities of STV and Condorcet rules.

The easiest way to tally CPO-STV is to start with the set of STV winners; drop 1 winner and substitute an STV loser. All voters who prefer this candidate over every candidate in the STV set prefer this new set of winners. All voters who prefer the dropped candidate over every candidate in the new set prefer the STV set of winners. CPO-STV tests all sets of [seats] candidates in Pairwise comparisons -- a Condorcet rule for sets of winners.

Thus CPO-STV drops a [liberal] candidate who has strong support from a plurality of liberal-party voters by replacing her with a liberal who is ranked higher by a majority of liberal voters. The replacement, who won few firsts and so was eliminated early in the STV tally, is agreeable to more liberal voters and likely to be more agreeable with non-liberal reps. CPO-STV may reduce negative campaigns among rivals with similar positions.

[CPO-STV is described briefly in Tideman 2000 and explained at length in a working paper mentioned in that article. His tests, using ballots from actual elections, show CPO-STV usually gives the same result as previous STV rules.]

[I think it is the best rule for giving STV “Condorcet consistency” and “non-negative responsiveness”. The later means a voter cannot hurt a candidate by raising her rank. Ballot sets have been concocted in which STV winner A becomes a loser if voter x raises his ranking of A. Such examples are exceptionally rare. The result might elect liberal B instead of liberal A. It is unlikely to change a council's balance from left to right.]

[Some STV supporters feel CPO-STV is so different from basic STV that is not a member of that family of rules. One could argue CPO-STV might not do what STV does best, that is: elect strong advocates for diverse policies.]

There few STV programs that can tally CPO-STV.

James Green-Armytage gives a simple example of an election in which CPO-STV elects a different set of winners than other forms of STV.

“One first excludes all candidates that are not in either outcome. Then one makes an initial allocation of votes among the remaining candidates, just as in the first stage of other STV methods. If no candidate has achieved a surplus, then the count is over. If there are any surpluses, these are distributed only if they belong to candidates who are in both outcomes being compared. After any surpluses have been transferred, the total vote for each outcome is the sum of the votes for the candidates in the outcome. The majority for one outcome over the other is the difference between the two totals.”

Tideman 2000:

Adapting CPO-STV

CPO-STV cannot guarantee election of the overall Condorcet winner unless sets of candidates lacking her are ignored. (It then could use the quota proposed for LER.) Such an ensemble of the Condorcet winner within CPO-STV (or in separate races) is an excellent rule for electing small councils directed to find balanced policies.

A very diverse community group I work with wants fair, proportional representation of interest groups, but some members also want a way to avoid electing people who don't get along with each other. They fear that an executive committee which fails to work together won't do its job well and may polarize a community. (On the other hand, when a diverse council does find get along, it can inspire the whole community.)

Bylaws could let each candidate declare with whom she refuses to work. This is done before the poll through a signed note to the election auditor and may require a public message too. Sets which contain incompatible candidates are not evaluated.

Both candidates (the disrespected and the disrespectful?) have less chance of election. A majority group could use this to exclude all candidates from a minority.

Weighted Ranked Pairs

In 2000 Bram Cohen suggested a different way of blending a Condorcet rule with a proportional rule. “You pick the first winner by Ranked Pairs, then for the second winner you use Ranked Pairs again, except that when comparing two candidates if a given ballot ranked the first winner higher than both of the two candidates being compared you lessen the weight of that ballot for that comparison. The formula for how much it's lessened is the same as the one used in STV.”

This is an ensemble rule because it 1) first elects the Condorcet winner and 2) then distributes the other seats rather evenly. But as mentioned for CPO-STV, a major goal for Full Rep or PR is to elect strong advocates from each major group. Condorcet rules such as Ranked Pairs would tend to fill those seats with more-widely-acceptable compromisers. The ballots that determine the first winner are from all voters, not just central voters; the winner is broadly acceptable. But central voters are the ones most likely to have their weights reduced when comparing candidates in the next round. The same pattern occurs in later rounds, though votes are less diluted with each round meaning candidates with less and less broad appeals can win.

Weighted Ranked Pairs also might serve as a Fair-share Spending tally. Ballots which “ranked the first winner higher than both of the two candidates being compared” divide the first winner's cost. It reduces their shares, but only for that comparison. Other ballots may have their weight shares reduced in the next one-against-one comparison. Unfortunately a majority group could fund a project that uses the entire budget, leaving nothing for the needs of any other interest group.

Minimum Rank Group, a Borda rule for sets

The Minimum Rank Group (MRG) evaluates candidates 1 set at a time. In an example for a 3 person committee, the first set holds candidates A, B, and C. Voter 1 ranked them as his forth, seventh, and second choices. The highest is second so a 2 is added to the set's running total. The addition repeats for each ballot. Then set A, B, D, is evaluated. The set that gets the lowest total wins.

A more general definition: Each voter ranks the candidates. Candidates are evaluated in sets and each set has as many candidates as there are seats to fill. Only sets of compatible candidates are evaluated. Each voter gives a set the points for his favorite candidate in that set. The set that gets the lowest total wins.

MRG is not a Borda Series. That elects the candidate with the highest personal Borda score, then the candidate with the next highest, the next, and so on. Like Tideman's CPO-STV rule, MRG evaluates sets (but without transfer of excess votes) so MRG too could be used when some sets are excluded.

Strategies: A ballot with a “bullet vote” for 1 candidate counts all others as tied for second -- so the bullet strategy does not work. A majority group's candidates could exclude every minority candidate, so allowing exclusions is not fair in a polarized community. Limiting each candidate to 1 exclusion helps only if the minority group can afford to run more candidates than the number of seats the majority party is likely to win.

The STV process of eliminations and transfers could cause a winner to lose if she were given a better rank by some voters. MRG avoids this esoteric problem of “nonmonotonicity” or negative responsiveness. It is seen in concocted examples. Nonmonotonicity with regard to 1 winner of a multi-seat election probably would not result in policies moving away from the direction intended by the voter.

[I think the central Condorcet winner is good for a board. Wide appeal and policy positions close to the median voter's make this the most appropriate candidate to moderate debates. Under Minimum Rank Ensemble (MREa), sets that do not include the Condorcet winner are excluded. The Condorcet winner may not exclude anyone from the council; anyone who declares an incompatibility is not eligible to become the chair. Otherwise she could dictate the entire council by excluding all but m-1 candidates. Under MREb the chair is elected and deleted from ballots before a MRG tally fills the remaining seats. Of course the chair may be filled through a separate election.

[It is good to keep some experienced people on the board while new members get up to speed. Your organization might give the sets overlapping terms. Each [3] member board overlaps for [1] month with the previous board, serves on its own for 11 months, and then overlaps for [1] month with the incoming board. (Probably during the budget process and annual meeting.) Wherever reps are chosen for their values and not for specific skills, the council may need to rely on a skilled and impartial staff.]

[[The Maximum Utility Group (MUG), which is similar to MRG, is very useful in simulations. It finds the set of m candidates with the highest utility score of all sets in the given electorate. That set's score forms a baseline when comparing the utility scores of councils elected by other voting rules. MUG takes far longer to calculate than any other voting rule in PoliticalSim. But for an organization with only a few hundred voters and 16 candidates it would take less than 5 minutes. Most of the computer code for MRG is available in PoliticalSim's MUG sub-routine. ]]

MRG is edited from a July 1997 email to Gordon at Twin Oaks Community.

Unequal Reps

There is a physical process somewhat analogous to the political organizing done by STV. “Selective Annealing” hardens metals through repeated heating and quenching. Each reheating takes the material to a higher temperature to break down the smaller metal crystals. Each cooling step allows the remaining large crystals to incorporate atoms released from melted crystals. The physics of the process is well understood and described in mathematics.

One might object that annealing leads to crystals of varied size and the election rule could lead to reps with different amounts of support. But STV can too, despite its care to transfer excess votes from a very popular candidate -- let's call her B. The voters who supported B gave some weight to their lower choices. But they would still say B is their favorite rep on the council, the one who most often speaks their views.

A large legislature could give each rep a voting weight (and salary) based on the number of ballots that rank her above any other rep. In some councils this can lead to a rep whose weight is too small to turn any losing coalition into a majority. So her support is never needed to form a majority and her power is zero.

In other situations a rep with little weight has as much affect as any rep. For example, a council has 7 reps. Ann has only 10% of the council's voting weight; each of the other six have 15%. Ann can turn any minority of 45% into a majority; she is needed just as much as any rep in a bare majority so she has as much power as any of them. Thus the voters who elected her are over represented and other voters are under represented.

There are several measures of voting power. Most rate the voter or voting bloc according to the percentage of coalitions that change from losing to winning with the addition of that voter or faction. See, for example, L. Shapley and M. Shubik, "A method for evaluating the distribution of power in a committee system," American Political Science Review 48 (1954), 787-792.) or Phillip Straffin. By these measures it seems weighted STV reps on simulated 5 seat councils always have equal power because there are never 2 reps with enough weight to form a majority, but any 3 can.

“In physics, models for thermodynamic phase transitions have been used for a number of years to study how marginal opinions are adopted by large groups in various social structures. It’s termed “opinion spreading” in the literature. ” https://www.reddit.com/r/science/comments/7t3sdd/a_simple_epidemiological_model_of_infectious/ mlmayo PhD | Physics | Mathematical Biology

“Thinking about that, it makes so much sense. In order for an idea to nucleate, it needs to reach a group of critical size before dying out. Once that size is reached, new individuals are "crystallizing" onto the idea faster than others are dismissing it.” Gryphacus

“"Critical size" here means the minimum self sustaining size.” -- Sasmas1545 -->

Enacting Policies

Weighted Interests

A voter can increase his power on issues he cares about by vote trading. It works this way: Voter 1 very much wants a left of center policy for issue T. He also wants a left of center policy for issue U but feels it is not so important. Voter2 has the opposite goals: she wants right of center policies and feels issue U is most important. They agree to change their votes on the issues they do not care about. So Voter1 knows there will be 2 votes cast for the left of center policy on issue T; and voter2 is happy knowing there will be an additional vote cast for the right of center policy on issue U.

Vote trading can, in theory, increase the utility value of the results. Voters trade away issues they do not care about, which are likely to be the issues they do not know well.

But vote trading has several problems.
1) Some people find trading partners; others don't -- so the distribution of power becomes uneven and unfair. One person might get 3 or more votes on an issue while another, who cares about it just as much, gets only 1 vote.
2) Bluffing, pretending to mildly oppose whatever a potential trading partner favors, is common. By pretending to “change” his vote (to exactly what he sincerely wants) a trader gets something for nothing.
3) Most trading is done in secret because some members of a trader's party would call him a traitor. Secret trading lets a voter trade away the same vote several times to naive voters.
4) If voting is done by secret ballots, there is no way to know if trade agreements are honored. Of course the mere possibility of such strategies increases suspicion and cynicism.
5) Trading can let 2 minority groups defeat the plurality group. It could counter with offers to trade votes with 1 of the smaller groups. But since they can form a majority and win without the plurality, they have nothing more to gain.

Democracy requires a clear public record of reps' votes on legislation, so voters may rate their reps. Vote trading confuses the record.

Reps in a legislature often trade votes but voters can't afford the days of bluffing and negotiating back-room deals. It would be better if each voter could weight his interest on each issue. A Condorcet tally can easily count a ballot as one and a half votes on one issue, and as half a vote on another issue.

[Cumulative voting (in which each voter gets as many votes as there are district seats and may give more than 1 vote to any candidate) gives no incentive for vote trading. It lets a voter cast as many votes as there are seats to fill. The voter may spread them out or give all to 1 candidate. The optimal strategy is to give all your votes to a candidate you like and who's chance of winning is about 50/50. You want to cast the decisive vote(s). This strategy includes decapitation, exaggeration, and free riding all in one. So it is not a great voting rule, particularly for weighting interest in issues. Cumulative voting gives very little information to the tally rule; more complete information leads to better social choices. In terms of information, LOR costs less than other systems because voters have less concern over strategies, how or whether to manipulate it, Vote trading is a move by some voters toward the cumulative voting strategy.

Here is a way of ranking priorities. It gives the benefits of vote trading while it discourages actual trades and avoids those problems. It gives a voter 1 vote on an average priority, extra weight on his top priority, and less than 1 on low priorities.

Many groups make most of their decisions in batches once or twice a year. This may be at an annual business meeting or a conference. The decisions made at this time include many different issues. A voter may have heavy interest in a few issues and light interest in others. He might be happy to give away his vote on a light issue to gain an extra vote on highest priority. For example, a parent of school children may want more weight than other voters on school matters. He might be happy to trade his vote on health care in exchange for an extra vote on a school policy.

Groups using consensus often develop a “squeaky wheel”, a person who asserts a need to influence every decision. Unrestricted point voting leads to the same thing: people who vote the maximum for many or all issues. The solution is the same in both situations. Ask the person &dquo;Which issue are you most concerned about?” He must declare his priorities, that is rank the heaviest interest as number 1. Ranks cannot be exaggerated. They will not be compared directly with ranks from other voters, only with this person's other ranks. So the voter cannot exaggerate intensities and would gain nothing by giving an insincere list.

{When there are few issues on the agenda, there probably is little need to prioritize them. So no priority vote is needed, all votes will equal 1. In effect a flat line slope is used. When there are many issues, voters are not likely to know and care about all of them. As the number of issues increases so does the desire to prioritize them and should so the line's slope.

{Suggested priority curves: from 1 to 4 issues no priority ballot; for 5 to 8 issues a line from 1.3 for top priority down to 0.7 for the lowest priority; for 9 to 12 1.6 down to 0.4 or the square root curve, and for more than 12 the square root curve or 2.0 down to 0.0.

{If the results of weighted and unweighted Condorcet tallies are the same, then no priority adjustments should be needed.

{Can adjustments be automatic for issues on which plain and weighted Condorcet give different results?

A good multi-candidate voting rule such as LOR is the key. It changes an issue from a series yes or no votes, to a continuum with a dozen proposals from left to right or up to down. Reps should not suddenly drop all weight from an issue just because their favorite is losing. If they did, the result could jump to a proposal even further away from their position.

It could work this way at an organization national conference: Each delegate 1) reads proposals, 2) listens to and debates issue number one. 3) ranks the proposed policies. 4) After ranking the last issue's proposals she ranks all the issues by their importance for her. 5) Vote yes or no on whether to allow adjustment. The adjustment ballots look like this:

ProposalRanks MovedUp or Down
asdfOOOOOUp or Down
qwerOOOOOUp or Down
jklblOOOOOUp or Down

A second adjustment, if called for, uses a ballot with fewer O's thereby allowing smaller moves. Reps may not suddenly drop all weight from an issue just because their favorite is losing.

[Who (in the majority) moves to counter a &dquo;minority surprise?” “You do.” &dquo;No, you.” ]

The convention must make separate decisions on several issues when it records votes. They may vote repeatedly, changing their weights for issues in response to the results of the previous tally. The policies that win round 1 might not win by many votes because the issue is crowded with similar proposals. Shifting weight from issue G to R may improve the policy for R but it may give G an even worse policy.

Voters rank each issue by its importance. A ballot counts as 1.9 votes for its number 1 issue. It counts as 1.7 votes for its number 2 issue, 1.5 votes for its number 3 issue, and so on. The convention is voting on 8 issues.

A voter has many desires, and only he can decide which have priority.

The utility function might discourage vote trading by making a traders loss at least equal to his gain. If he gains a third place vote he should loose a third place not an seventh place.


Key for Charts, 7K
Items	Priority	 Ranks

Ballot 1 Ballot 2
A 14 B 23 C 31 D 45 E 52 F 68 G 77 H 86

No utility differences, 9K Small utility differences, 9K
Charts 1 - 2) No Priority Differences, Utility = 1
Charts 3 - 4) Small Priority Differences, Utility = 1.3 - ? × Priority number
No utility differences, 9K Small utility differences, 9K
Charts 5 - 6) Moderate Priority Differences, Utility = 1.6 - ? × Priority number
Charts 7 - 8) Moderate Priority Differences, Utility = = 2 - 1.5 × SqRt (Offer) / SqRt (Priority number)
Increasing utility values, 9K
Charts 9 - 10) Big Priority Differences, Utility = 2 - 0.25 × Priority number.
The general formula is Utility = 2 - (0.5 × number of issues) × X.

These graphs do not show which proposed policies each voter prefers. The 2 voters might agree about which proposed policy would be best for issue T. All these charts tell us is that the 2 voters disagree about the importance of issue T.

Vote trading does not work well at an annual meeting or conference. Voters there don't know each other well; bluffing is easy. They cannot check whether a trading partner kept his side of the bargain, or how many times he traded away the same vote.

There is a maximum line from (0, 2) to (1.0, 0.5) to approximately (0.4, 1.0).

You cannot exchange your a full vote on a low priority issue for a full vote toward your top priority. If you give a low priority, then you get only a fraction of a vote. What you give is what you get. To get a significant vote you must give up a significant vote. You can exchange your number 2, worth 1.2 votes for someone else's. But then your real number 2 is pushed down; and so are all of your other priorities. You gain 1.2 for #1 but lose 0.1 for all of the others – [ which adds up to more than ] And your constituents might see that you ranked a low priority #2 and gave it a bad policy! No free lunch there.

Low priority, low interest, little information and thought, therefore little voting weight. Getting people to not vote on issues they don't care much about can improve those decisions. Many people neglect voting but few are willing to deny themselves the power to vote on every issue.


Two voters could trade votes on second-rank issues. Each would change 1.5 votes for his number 2 goal into 1.5 votes against it. In exchange he would get 1.5 votes for his number 1 goal. But what they give is equal or nearly equal to what they get. The reward is less but the cost of time spent negotiating is constant.

Divide and conquer strategy: Get 2 groups in a hot fight over [economic] policy. Use rumors or secret donations or anything else to split the opposition in two. Each faction will give their top priority to [economic] issues while the strategists top-rank and win control of [social] policies. A second vote that lets reps readjust their priorities would not help the majority prevail on [social] issues because the 2 major groups would continue their battle on other issues.

Majority reps may be tempted to take a free ride on the votes of other majority reps. They could do that by giving a low priority to issues they feel are certain to win. This trick lets them give first priority and maximum weight to a less popular issue. To reduce that incentive, Condorcet's rule could find the top 1 or 2 issues and then tally a winner for each. Those issues would be deleted from all ballots before figuring the weight of each issue on a ballot. (The same might be done for the issue whose Condorcet winner has the biggest margin of victory over its nearest rival. But this requires re-running all of the tallies after finding the 1 with the biggest margin.)

The priority voting helped if: 1) Its results were not the same as Condorcet tallies without priority weights. 2) A majority of voters preferred the results of priority-weighted voting.

Ballots could be weighted according to seniority, test scores, or past performance. That use is outside this web site's concern with ways of counting votes. It threatens to revive the sort of “democracy” common in late Nineteenth Century Germany. There, each man's voting weight equaled his taxes. In some towns a factory owner, and factory directors he appointed, paid a majority of the taxes and cast most of the votes. The council majority thus was appointed by the richest man in town. “Voting” of this sort did not create legitimate governments or social peace.


The multi-winner allocation rule LAR introduces other innovations to reduce the importance of the elimination sequence, just as immunity does. There may be a way to make them help LOR to resist manipulation. But they do not resolve voting cycles so they cannot prevent that manipulation. Unlike STV, they are 100% Condorcet efficient. That means whenever there is a Condorcet winner, these rules find and elect her.

LORr runs a LORu or STV tally. Then STV is run again, but this tally will release votes for previous losers ranked above the previous winner. When a vote for an item is released (suspended or by-passed) the weight is still offered but not reserved. That means a ballot offers that weight to its next preference also. The item with the fewest votes has those votes released. (STV would eliminate that item.) The losers may be released 1 at a time and the previous winner may not win until all losing votes have been released.

An item, C, may have votes released repeatedly as votes for other items are released and some ballots transfer weight down to C. When a ballot's losing votes all have been released, its weight is offered to those items and to the winner of the previous tally. When no weight is reserved for losers on any ballot, then the winner of the previous tally may win. A loser of the previous tally can win if it gets 50% by the time all losing votes are released. If the winner is not the same as the previous tally's winner, the process may be repeated. The web page on allocations explains suspend and release in more detail.

LORo omits obstructions, they do not win by STV but they change which option does win. These are often wedge issues used to divide and conquer. They often squeeze out more central options. In the example above, B wins so it does not obstruct. If A or C were omitted, B would still win so they do not obstruct. But if D were omitted, C would win, so D does obstruct. Dropping it lets C win. (In this case there is a Condorcet winner, C, and LOR can find it on a table of pairwise tests.)

                          ballots for :
LORo D omitted    step    A   B   C   D     action          .
                   1      2   2   3   -     transfer A's ballots
1 to B, 1 to C     3      -   3   4   -     C wins a majority
In some situations LORo is terrible: it makes a virtue of weakness. In some 3-way voting cycles the first interest group eliminated sees it second choice win by STV. Their favorite, F, and the winner, S, are not obstructions but their last choice is. That group's last choice L, is omitted. If most of L's ballots give second preference to F then LORo makes their first choice the winner! It is easy to give away firsts to make one's favorite the weakest and first eliminated.

LORo is not yet programmed in PoliticalSim and so its statistical tendency is unknown for elections with many voters and candidates. The research version of PoliticalSim will not include LORo and strategic voting for some months. LORe, is in PoliticalSim.

Funding Projects

This section gives brief views of several voting methods for project funding. The Loring Allocation Rule was explored first because its seems to result in high quality and equity with broad support. But each rule may have some advantage over others. For example, the Minority Funding Process explained here is slow but very flexible and does not need a computer. This is just a collection of notes, not even a rough draft. Your constructive criticism is needed and welcomed.

Minority Funding Process

The Median Voter Process asked each rep how she would fill the entire budget. The Minority Funding Process asks each rep how she would fill one-tenth to one-third of the budget. In this way MVP works like bloc vote and MFP is like limited vote (as noted below *.) A rep gives each of her favorite items the amount she thinks it needs -- knowing that some other items will be funded by other reps. Each must prioritize and budget her many competing interests. Voting only a fraction of the budget develops realistic expectations about the limited effect a person usually has on decisions by a diverse group.

The by-laws or rules of the meeting require each item to win funds from a minimum number of reps: one-tenth to one-third -- the same as the fraction of the budget voted by each rep. This also becomes the maximum fraction that 1 item can win.

Each item's sponsor suggests a recommended budget for it. The by-laws specify a range of allowable preferred budgets such as 25% to 300% of the suggested amount. The sponsor may set a narrower range or a fixed price.

An item must win support from a large minority. It is funded at the average amount they voted for it.

An item can win more than enough supporters. Then those who voted to give it a small budget are not among its top supporters. They are hurting themselves if they do not move their funds to raise the budgets of some other item(s). The excess low votes should be transferred.

[ *To understand this new funding rule, it will help to understand 2 old election rules: bloc vote and limited vote. Both are used in “at-large” elections. For example, a 5 seat city council in which all candidates compete in 1 city-wide district. The candidates who get the most votes win. Bloc vote lets a voter cast as many votes as there are seats to fill. He may give only 1 vote to a candidate. A majority group with 5 candidates for 5 seats wins all 5. No other candidate can win more votes. Limited vote lets a voter cast fewer votes. Each voter in a 5 seat district might cast 3 votes. If the majority gave all its votes to 3 candidates they would win that majority -- but not all of the seats. Limited vote often results in proportional representation. But if the majority's votes were evenly divided among 5 candidates, most could lose. Plurality rules that lack candidate elimination and vote transfer leave a group split by too many candidates. ]

MFP's process avoids plurality-rule problems. The process is a sequence of votes, requiring progressively higher numbers of supporters. After each step, the item with fewest supporters is eliminated, like the weakest candidate in an STV tally; reps then transfer their allocations from the loser to the remaining items.

Most point-voting rules offer easy strategies: the punishing votes and exaggerations explained in the pages on elections. But MFP has conflicting incentives. A version of this has been used for several years by a 100 voter group in Virginia. They find the incentive to exaggerate for one's top preference is more than off-set by the incentive to spread out one's vote and create as many winners as possible. Some ballots have several minimum votes but maximum votes are few. Most votes are not at the extremes.

MFP Variations
Rule Number
of Groups
Voters in
% of
MFP 3 33 33 33
MFP 2 54 25 25
MFP 2 05 20 20
MFP 1 19 11 11

MFP Variations
.	Number	Minimum	Voter's	%
Rule	of Groups	% in Group	of Budget
MFP	3	33	33	33
MFP	2	54	25	25
MFP	2	05	20	20
MFP	1	19	11	11

Voters usually won't form such distinctly separate groups. Instead, interest groups will overlap on many proposals.

This process is like the Median Voter Process.
Set rules for the voter's percentage of the budget and the range of allowable $ votes.
Design ballots listing items with their suggested and minimum amounts. Leave several columns for $ votes and revisions.
Introduce MFP: “Each item needs at least [25] supporters to win. Items with less than [25] will be eliminated, 1 at a time. Move your $ from losers to remaining items.”
Tally how many reps support each item on the first vote. Track additional supporters after each elimination.
Find the decisive [25]th voter for each item. Remind reps with lower $ votes to move their funds and ask them to name any newly-supported item so its tally can be increased to avoid elimination.
Eliminate the weakest item. If several items tie for elimination: A) Ask reps who voted for 2 or more of the tied items, “Which of those would you drop?” Eliminate the 1 with the weakest support. B) Use Condorcet's rule. Eliminations force reps to move $ votes more often than in MVP. Conducting an MFP Vote

Joint Allocation Rule

Twenty people picking 5 pizzas from 30 on a menu could use another rule like STV. The Joint Allocation Rule adapts STV for collectively buying personal goods in bulk lots.

We might talk of “buying shares in an item” instead of “offering to contribute to it.”

Maximum Utility Rules

The January '97 version of PoliticalSim introduced three election rules for simulation research. Spatial models for political simulations define “utility” as proximity. The Maximum Utility Candidate (MUC) is the one whose total of distances to all voters is the shortest. That is the candidate closest to the average voter. The Maximum Utility Series (MUS) fills the council with that candidate and the next best and so on. The Maximum Utility Group (MUG) elects the council that best distributes representation so each voter has a nearby rep. The Maximum Utility Ensemble (MUE) is analogous to LER: the MUC takes the place of the Condorcet winner as chair and MUG takes the place of STV in electing the reps.

MUE can adapt to be an allocation rule like LAR. If an item wins funding, its fund will be its average $ vote. MUS uses [15]% of the budget; MUG uses the rest. For MUG, a social-utility score must be tallied for each set or combination of projects that fit within the budget. Each ballot searches a set for favorite items totaling [20]% of the budget. The ballot's scores for those items are totaled and added to the set's score.

If an item is not in the top [20]% of the budget on at least [20]% of the ballots, then it does not meet the quota requirement. The one with the fewest supporters is dropped from the set and the set's score is calculated all over again. The set with the best score wins.

The most obvious problem with MUG is the time it takes to test every possible set of winners.

All utility rules have a major problem: By moving a large distance to one side, extremist voters have a large effect on MUC's winner -- more than on Condorcet's. MUC elects the candidate closest to the average voter. Condorcet's rule elects the candidate closest to the median voter. (A median does not change as extremes become more extreme.) This shows the utility rule's vulnerability to manipulation by exaggerated and punishing votes. Of course MUG is not nearly as good as STV, the rule most resistant to manipulation. When reps vote strategically the outcome of a utility rule cannot reach it potential high utility value. But it is useful as a benchmark when comparing more practical rules.

Standardized Score Rule

In Making Multi Candidate Elections more Democratic, Samuel Merrill III. suggests a better way of voting with scores. It limits and discourages the exaggeration elicited by most scoring rules. The rule spreads each voter's scores on a bell-shaped ”normal distribution” to limit exageration.

The normal curve fits many patterns observed in nature: the height and weight of teachers, or of bananas. But there is no reason to suppose a voter's preferences on a particular ballot should fit this curve: strongly for one, luke warm or cool toward many, and strongly against one.

A voter can try other patterns, but if she strongly favors 2 candidates or expensive projects, neither will get the highest score possible. (As you can see, only a little one would fit out in the “tail”). Both votes would be adjusted toward the center. So, as Merrill explained, it pushes a voter to carefully assess the situation and vote strategically.

The ballot needs to be on a computer so a voter can see both her raw scores and her standardized scores. PoliticalSim offers players Standardized Score voting on thermometer charts as a way of selecting the election rule.

Adjusting a ballot's scores to fit into a bell curve is not as flexible as allowing a personal utility curve made from ratios of the voter's scores and limited to one vote. It might lead to single-winner rules even better than Condorcet or Borda, but for most voters it is for now less practical.

- - - - -

Standard-score rule asks voters to rate candidates on a fixed scale, say 0 to 10. It then makes each voter’s ratings average zero (some ratings become negative). It also “normalizes” the variation within a voter’s ballot.

If voters accurately guess each candidate’s chances and then vote carefully, this system can select the candidate with the maximum utility to the electorate. A voter may give a big score to one item and very small negative scores to all other items. Or she may give moderate plus and minus to many items.

“...for each voter separately, replace her ratings ri by their statistical standard scores, i.e.,
Zi = (ri - u)/s
where u and s are the mean and standard deviation of the voter’s ratings.”

“The standard- score system, because of the complexity of its decision rule, should be recommended only for a mathematically knowledgeable electorate.” (Samuel Merrill, 1988, pages 101 and 103) It is hard for a voter to estimate the size of his votes.

As with many voting rules, each voter needs to calculate every candidate’s probability of tieing for the win and then try to make his or her votes tip the balance.

Strategies: Punishing votes give very low scores, -3, to rival motions. Bullet votes give the maximum score, +3, to only 1 item. If the first choice loses, then the rest of the ballot's scores do not help the voter's other favorites. So the best strategy suddenly becomes the worst. Standard Score also can be manipulated in a way very similar to Hylland- Zeckhauser.

Dr. Merrill suggested Standardized Scores for single-winner decisions, not for multi winner elections or budget setting.

A simplification can reduce exaggerated ratings of comments.

Agent Allocation Rules

Each ballot acts as an agent trying to maximize the value of the outcome for its voter. Input varies according to the voter's preferences. An agent has less information than its voter about his preferences but more time and information about other voters. MVP agents, for example, search for other agents to negotiate vote trades. LAR agents search for others to form the minimum needed for winning. Simulation techniques can evolve new agents through differentiation and selection of successful ones.

Comparing Funding Rules

Political scientists, mathematicians, and economists have tried for decades to create rules for Proportional Allocations (PA). But all have failed, often because a coalition could manipulate the results. (In fact, several researchers have found mathematical proofs that no voting rule can promise to always meet various reasonable criteria; so no rule can be perfect.) Still, in order to buy public goods such as roads and schools, we need to find the best rules possible. The best ways to compare voting rules are case studies and computer simulations like PoliticalSim.

Voting Rules
Qualities MVP MFP LAR JAR Private
Min. Decisive Group 51% 20-33+ 20-100 2+ 1
Ballot % of Budget 100 20-33 100+ - Private $
Largest Item's % 100 20-33 100 100 100
Smallest Council 9 21 21 9 1
Biggest Council - - - - 1
Free-rider Problem small big small none none
Equal Voters Yes Yes Yes no no
Time Cost mid long short short short
Teaches - - - - -
    Budget is limited. Yes Yes - - -
    Projects are costly. -- -- - - -
    Shares are limited. -- -- - - -
    Rank priorities. Yes Yes - - -
Public Goods Yes Yes Yes no no
    Departments Yes maybe - - -
    Projects OTRAs no Yes Yes - -
Examples - - - - -
    Fire Bldg. code - - - - -
    Insurance Disaster Group Individual - - -
LAR versus MFP: LAR increases the number of people who share the cost of a popular item, so it costs each person less; increases the average number of items a person contributes to; increases the number of top-ranked items that low bidders contribute to; decreases the $ per item. MFP lets voters deal with 2 of a kind.

The Minority Funding Process is quite adaptable, but its repeated votes are time consuming and demand voters' close attention. Movable Money Votes let voters simply rank the options and it lets voters, not sponsors, set an item's budget. The tally is complicated and no one has yet written tally software. Further research, including computer and workshop simulations of voting, is needed to evaluate, compare, and develop rules for proportional allocations.

Setting Budgets

Minority Power and Departmental Budgets

The Loring Allocation Rule also might add to ongoing budgets for departments: The ballot below has a box for each $1,000 added to each department. (The voter does not mark his preferred budgets because each item has a set cost of $1,000.) A voter might give first and second priority to the first and second $1,000 for department S, third priority to the first $1,000 for department R, forth priority to H, and then more for S, or R, and so on.
Prioritize New Funds to
Town Departments
Money in Thousands
  Dept.   1 2 3 4 5 6
Council J -- -- -- -- --
Fire F O -- -- -- --
Health D N -- -- -- --
Parks K -- -- -- -- --
Police H P -- -- -- --
Roads C G M -- -- --
Schools A B E I L --

The ballot would grow too long if it held many accounts. Therefore, reps first set budgets for departments. Then they vote to divide a department's budget among its agencies. Each rep's weight in that vote is the amount she contributed to the department.

If a rep has weight leftover in the vote for agencies of department G when other reps have none, she cannot create a quota and her weight is unusable. This leftover weight might go into the department's general fund. Or the rep may use it in a later vote for another department. Perhaps the last “department” should be tax, deficit, or debt reduction.

As each vote nears, the rep negotiates and trades votes to find a quota for her favorite agencies. She does not need to find a majority. It is both a plus and a minus that proportional budgets reduce the emphasis on broad agreements. (Broad agreements are still needed for enacting policies.)

LAR can give a clear record of each rep's allocations. This helps voters evaluate the voting records. Reps cannot hide their priorities within parliamentary maneuvers. And parliamentary maneuvers cannot block a group's priorities.

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